Question: Solve for $x$ and $y$ using elimination. ${-x-4y = -28}$ ${x+5y = 34}$
Answer: We can eliminate $x$ by adding the equations together when the $x$ coefficients have opposite signs. Add the equations together. Notice that the terms $-x$ and $x$ cancel out. ${y = 6}$ Now that you know ${y = 6}$ , plug it back into $\thinspace {-x-4y = -28}\thinspace$ to find $x$ ${-x - 4}{(6)}{= -28}$ $-x-24 = -28$ $-x-24{+24} = -28{+24}$ $-x = -4$ $\dfrac{-x}{{-1}} = \dfrac{-4}{{-1}}$ ${x = 4}$ You can also plug ${y = 6}$ into $\thinspace {x+5y = 34}\thinspace$ and get the same answer for $x$ : ${x + 5}{(6)}{= 34}$ ${x = 4}$